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quasi-geodesic

Proceedings of the Edinburgh Mathematical Society (1)

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Location of geodesics and isoperimetric inequalities in Denjoy domains
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José M. Rodríguez, José M. Sigarreta
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 1 / February 2012

Published online by Cambridge University Press:

15 June 2011, pp. 245-269
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We find approximate solutions (chord–arc curves) for the system of equations of geodesics in Ω∩ℍ for every Denjoy domain Ω, with respect to both the Poincaré and the quasi-hyperbolic metrics. We also prove that these chord–arc curves are uniformly close to the geodesics. As an application of these results, we obtain good estimates for the lengths of simple closed geodesics in any Denjoy domain, and we improve the characterization in a 1999 work by Alvarez et al. on Denjoy domains satisfying the linear isoperimetric inequality.